Actually, the Austrians were invited to Berlin in 1883. However, they were merely there as observers, not active participants.

The Habsburg Empire has always been a land power, whose primary rivals were Russia and the Ottoman Empire. Germany, in contrast, saw her mortal enemy as France. France had colonies, thus Chancellor Otto von Bismarck believed absolutely that in order for Germany to be taken seriously by France (despite their trouncing of France in 1870-71), especially as a new nation, it needed various prestige projects, including African and Pacific colonies. The Austrian Empire (after 1867 the Austro-Hungarian Empire) simply had no interest or need to go abroad. There reasons were manifold.

Firstly, you have the person of the Kaiser himself, Franz Josef. During his reign, people lived and died without knowing a single other monarch. He gained the throne in 1848, and did not die until 1916. He came to the throne at eighteen and was not intended to ever take the throne, but after Emperor Ferdinand was deposed in 1848, and Franz Josef's father, Franz Karl was found to be unsuitable to the throne. To quote András Gerő in "Emperor Francis Joseph King of the Hungarians":

"The head of the Habsburg family, the emperor [Ferdinand], was not exactly a manly character, and his feeble-mindedness, which in peacetime could be patiently tolerated was, at a time of crisis, nothing but a source of humiliation for his relation... Francis Joseph's father [Franz Karl] was a jovial type, lacking in fortitude who - as his reaction to the political upheavals demonstrated - failed to live up to the principle that Metternich so consistently insisted upon: he had no authority - all he could do was drift with the tide. His younger brothers [Ferdinand Maximilian, Karl Ludwig, and Ludwig Viktor] were of no help to Francis Joseph either and of little consequence." (Gerő, page 35). Notes in brackets in the above quote are my own addition for context and clarity.

In the European context, colonies offered a sort of liberty, a sort of promise that seemed too revolutionary to this hyper-conservative, reactionary, monarch. The popular mindset of colonies, especially in Africa, was that of something of a European version of the American Wild West, a land of untapped resources, limitless possibility, savages that needed civilizing, and a chance to start anew. Colonies to most of Europe were an outlet of imperialist ambition. For much of Franz Josef's reign, Austria was preoccupied with the Kaiser's reactionary paranoia stemming from the circumstances that surrounded his assumption of the throne. It took all of the nation's focus through all of his life to keep the Empire from falling apart, without factoring in any sort of crazy colonial adventures.

Which brings us to a second reason for the disinterest by Austria-Hungary for African colonies. In the eyes of Vienna, Austria already had an empire. She had no need for more, and indeed, after the Ausgleich (The Compromise of 1867), her focus was on internal stability. Austro-Hungarian geopolitical strategy was not about power projection but about the maintenance of the Status Quo. What little imperial ambition that Austria had historically been satisfied at the expense of the Turks, and what few ambitions Austria-Hungary did have after 1867 did come at the expense of the Turks or the Russians, usually by intervening in the peace process, as I'll elaborate on shortly.

Austria saw her role as ensuring that the world remained, more or less, exactly as it was, in perpetuity. Austrian politics saw that the balance of power was something that would be decided in Europe itself. Any overseas adventures for colonies would be draining and distracting from the European main theater, where Austria was already hard-pressed to fully focus on maintaining the continental balance of power. The fact that Austria passed on intervening alongside her historic ally, Russia, in the Crimean War was the first proof of Austria's vanishing omnipotence, and after the Crimean War, it'd take all of Austria's focus to simply avoid a long, slow, and very painful decline. Austria had only minimal 'imperial' ambitions after 1867, and its ambitions were less about gaining land for itself, and more about trying to stymie nationalism.

Take, for instance their role at the Congress of Berlin in 1879 (not to be confused with the Conference of Berlin, in 1883 that concluded the Scramble for Africa). At Berlin, seven nations and twenty diplomats met to settle various disputes, primarily the recent Russian victory over the Turks in the Russo-Turkish War of 1877-78. These nations comprised of Austria-Hungary, France, Italy, Turkey, Germany, Britain, Russia. Each of the European powers sent three diplomats, Turkey sent two. Austria-Hungary's party consisted of "Count Andrassy, a man of quick apprehensions and slow resolves. Beside Andrássy sits Count Karolyi, perpetual Austrian envoy in Berlin... The third member of the Austro-Hungarian delegation is Baron Haymerle, a Viennese, about whom everything is sharply pointed, from his nose to the pencil with which he takes his notes." (Emil Ludwig, translated by Eden and Cedar Paul. "Bismark: the Story of a Fighter" p 516. ). Andrássy's goal was to cut off any Russian territorial ambitions at the knees, and to spoil any goals of pan-Slavism that could rouse the Slavs in Austria-Hungary into sympathetic rebellions. In doing so, Austria had to spend much of its political will and capital simply to prop up the Turks and oppose the Russians.

This is not to say that Austria-Hungary never embarked on colonial adventures of any sort however. She did send soldiers to Mexico to support Maximilian I (Ferdinand Maximilian), and also sent 4 warships and 300 marines to support the Eight Nations Alliance during the Boxer Rebellion. However, in Mexico, France did most of the heavy lifting, with the Austrian contingent coming late (1864) and also numbering barely 1100 men. During the Boxer Rebellion, only one warship and and her marine complement actually participated in any combat operations since the other three vessels had to be called up from the Mediterranean. In 1883, the Austro-Hungarians were invited to the table as observers to the Conference of Berlin to carve up Africa. Despite their disinterest in actively participating, their size and importance in European affairs ensured a place at the table.

In short, Austria-Hungary simply had no had capacity, no interest, to seriously look abroad when its own internal issues and its own geopolitical strategy did not afford any sort of opportunity to indulge in the colonial experiment. And while some in Austria-Hungary may have wanted colonies, Franz Josef was such a commanding figure that his disinterest put the final nails in the coffin.